I pretty sure you cannot create a new account using facebook gameroom. You would have to start a game on other device (iOS, Android or BlueStacks) and then connect that device to your facebook account.

Also, be careful many people reported issues with multiple accounts and fb gameroom. I personally had my accounts screwed up so I had to stop using gameroom (I use Bluestacks on a Windows PC instead)

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Try Memu. It's an emulator that lets you create multiple instances. Each new instance should create a new account, then you can link them with FB.

I just use an iPad. Every time Zynga does an update I have to uninstall and reinstall, so I have like 11 accounts, but I have only really used 6. Reinstalling the app on a mobile device also creates a new account. I've never tried, but I'd bet that simply clearing all the app data on an Android device would create a new account too. But make sure you are connected to Facebook first so you don't lose your primary account.